Could space travelers melt as they accelerate through deep space?

Forty years ago, Canadian physicist Bill Unruh made a surprising prediction regarding quantum field theory. Known as the Unruh effect, his theory predicted that an accelerating observer would be bathed in blackbody radiation, whereas an inertial observer would be exposed to none. What better way to mark the 40th anniversary of this theory than to consider how it could affect human beings attempting relativistic space travel?